This paper considers the problem of source coding with side information at the decoder, also called Slepian-Wolf source coding scheme. In practical applications of this coding scheme, the statistical relation between the source and the side information can vary from one data transmission to another, and there is a need to adapt the coding rate depending on the current statistical relation. In this paper, we propose a novel rate-adaptive code construction based on LDPC codes for the Slepian-Wolf source coding scheme. The proposed code design method allows to optimize the code degree distributions at all the considered rates, while minimizing the amount of short cycles in the parity check matrices at all rates. Simulation results show that the proposed method greatly reduces the source coding rate compared to the standard Low Density Parity Check Accumulated (LDPCA) solution.

This paper investigates channel coding for DNA data storage, a recent and emerging paradigm in which both substitution errors and synchronization errors (insertions, deletions) are introduced in the stored data. The paper first proposes a novel and accurate statistical channel model to represent errors introduced by the DNA data storage support. The channel model takes the form of a k -order Markov Model which allows to capture both memory in the sequence of channel errors, and statistical dependency between errors and input sequence. The model probabilities are inferred on two sets of data: one set of experimental data, and one set of genomic data. In both cases, we observe a superior accuracy, evaluated from the Kulback-Leibler divergence, of our channel model compared to existing ones. Second, the paper investigates the design of error-correction solutions dedicated to the proposed channel model. It considers a concatenated code construction built from a convolutional decoder which aims to correct synchronization errors, and from an outer LDPC code which corrects residual substitution errors. While this construction was already investigated for i.i.d. errors, this paper shows how to include all the knowledge of the proposed channel model into the convolutional decoder. Numerical results show that the proposed decoding algorithm significantly improves the decoding performance in terms of BER and FER, at the price of an increased decoding complexity.

This paper explores the emerging field of in-memory computing, which has the potential to significantly improve energy efficiency in many signal processing and machine learning applications. In-memory computing systems are impacted by various sources of noise and perturbations that can affect their computation accuracy. Therefore, this paper aims to identify the key challenges to be addressed from an information-theoretic point of view in this area. It first identifies relevant computation structures and noise models from the literature of hardware implementation, and then reviews existing works in information theory and error-correction for in-memory computing. Finally, it identifies key open avenues for establishing information-theoretic foundations of in-memory computing systems, and for providing insightful design rules leading to highly energy-efficient computing systems.

This paper considers iterative dot-product computation implemented on in-memory memristor crossbar substrates. To address the case where true memristor conductance values may differ from their target values, it introduces a theoretical framework that characterizes the effect of conductance value variations on the final computation. For simple dot-products, the final computation error can be approximated by a Gaussian distribution; the mean and variance values of the corresponding Gaussian distribution are provided. For iterative dot-product computation, recursive expressions are derived for the means and variances of the successive computation outputs. Experiments verify the accuracy of the proposed analysis on both synthetic data and on images processed with memristor-based principal component analysis.

This paper presents in-depth rate-distortion and outage probability analyses for two-stage successive Wyner-Ziv (WZ) wireless communication networks. The system model assumes Lossy Forward (LF) cooperative communication where lossless reconstruction is not necessarily required at the relay. This paper aims to quantitatively derive the relationship in distortions between the Source-to-Destination and the Source-to-Relay links. Hence, the design parameters are the distortion levels at the relay and destination. The admissible rate-distortion regions are first analyzed for the two stages separately, where the relay is referred to as Helper. The rate constraints with the links involved in the end-to-end (E2E) communications are then derived. Distortion Transfer Function (DTF) is introduced as a mathematical tool for analyzing the distortions of networks having multiple stages. It is shown that the higher the correlation between the Source and Helper observations, as well as the larger the E2E tolerable distortion, the larger the admissible rate region. The outage probability of the two-stage successive WZ system is evaluated, assuming that the second stage suffers from block Rayleigh fading while the first stage performs over a static wireless channel. The E2E outage probability is also analyzed with the distortion requirements at Helper and Destination as parameters in independent and correlated fading variations. It is demonstrated that the decay of the outage probability curve exhibits a second-order diversity in a low-to-medium value range of average signal-to-noise ratios (SNRs) when the helper distortion is relatively low. It is shown, however, that as long as the reconstruction at Helper is lossy, the outage probability curve asymptotically converges to the decay corresponding to the first-order diversity at high average SNRs.

In this paper, we consider the construction of a Slepian-Wolf source coding scheme in a context where only a small amount of data has to be transmitted to the decoder. In this context, we propose a novel rate-adaptive Slepian-Wolf code construction that is based on non-binary LDPC codes. The construction we propose replaces the regular accumulator of the standard LDPCA method by a local graph that is optimized at every rate of interest. In our method, the local graph is specifically designed in order to give good decoding performance at short length, while existing LDPCA constructions are usually optimized under an infinite codeword length assumption. Our simulation results on short codes obtained from our design method show a FER improvement of up to an order to magnitude compared to the standard LDPCA construction.